Hmm, ok, It helped on mine.
It sounds to me that the audio mute that Uniden is using is not completely muting so you are getting the white noise between transmissions. You could try an external sound gate (VOX), the problem is the delay in turning on will often lose the first syllable of the message (I have a cheap blue-tooth head set that I tried to use to listen to audio books on my phone that does this and is very annoying).
Try to pad the audio down to the point the recording amp doesn't pick it up.
If you are really into hacking, most of the audio chips have an actual mute line on them that can be attached to the squelch line to mute the noise. It is usually ignored because the level is too low to be heard over the speaker and the couple of cents to route the signal and decouple it add up during manufacture. I had to modify some early BK two-way radios that the officer didn't like the chuffing while it scanned.
One of those annoyances that is tough to remedy.
Bruce